Coherent States for Tremblay-Turbiner-Winternitz Potential

TL;DR

This paper constructs coherent states for a particle in the Tremblay-Turbiner-Winternitz potential, linking quantum states with classical orbits, and deriving energy eigenstates for this specific potential.

Contribution

It introduces a method to build coherent states for the TTW potential using conserved charges of four harmonic oscillators in polar coordinates.

Findings

Coherent states follow classical particle trajectories.

Energy eigenstates are explicitly derived.

The approach links quantum states with classical dynamics.

Abstract

In this study, we construct the coherent states for a particle in the Tremblay-Turbiner-Winternitz potential by finding the conserved charge coherent states of the four harmonic oscillators in the polar coordinates. We also derive the energy eigenstates of the potential and show that the center of the coherent states follow the classical orbits of the particle.